I think I can answer your question, because I asked an identical one on bitcoin.stackexchange.com about a year back.

The transactions are public because that's the only way account balances can be tracked in this system. There's no 'amount' associated with an account id at any point in time, as there is for a banking database. In Blockchain, all the money an account has to spend is the net of the transactions made to and from that account. In traditional banking, even if you deleted the transaction history, it would work, because the account balances would be correct. This incentives people to fudge the history and the final balance via fraudulent transactions. Blockchain prevents that, since it never stores the balance, and old transactions are set in stone.

As to your second point, yes, mapping the wealth is possible. But so is obscuring the account holder's ID. To get your money, you just need a private key, a little string of characters, to verify that account. Also, account creation is incredibly easy (literally just a function call returning a 256-bit hash). So, no one knows who is who on the network. Some transactions may go from a person to themselves, others may go from a person to another for services rendered. It's basically impossible to tell once the transaction volume grows large enough.